What is the imaginary unit $$i$$ ?

The imaginary unit $$i$$ is defined as $$i = \text{sqrt}(-1)$$ . It is used to extend the real number system to include solutions to equations that do not have real solutions.

Simplify $$\text{sqrt}(-x)$$ where $$x > 0$$ .

$$\text{sqrt}(-x) = i\text{sqrt}(x)$$ .

How do you subtract two complex numbers, e.g., (7 + 3i) - (2 + 5i)?

To subtract complex numbers, subtract the real parts and the imaginary parts: (7 - 2) + (3i - 5i) = 5 - 2i.

Multiply the complex numbers: (2 + 3i)(4 - i).

Using the distributive property: 8 - 2i + 12i - 3i^2 = 8 + 10i + 3 = 11 + 10i.

What is the conjugate of a complex number $$a + bi$$ ?

The conjugate of $$a + bi$$ is $$a - bi$$ .

What is the modulus of a complex number $$a + bi$$ ?

The modulus of a complex number is given by $$|a + bi| = \text{sqrt}(a^2 + b^2)$$ .

Solve the equation $$x^2 + 49 = 0$$ .

The solutions are $$x = \text{±7i}$$ .

Simplify $$\text{sqrt}(-108)$$ .

$$\text{sqrt}(-108) = 6i\text{sqrt}(3)$$ .

Complex Numbers

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Mathematics

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11th - 12th Grade

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Practice Problem

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Hard

•

CCSS

HSN.CN.A.1, HSN.CN.A.2, HSN.CN.A.3

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FLASHCARD QUESTION

Front

Define a complex number.

Back

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

Back

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

Back

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

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CCSS.HSN.CN.A.2

FLASHCARD QUESTION

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Back

FLASHCARD QUESTION

Front

What is the standard form of a complex number?

Back

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CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

How do you add two complex numbers, e.g., (3 + 4i) + (5 + 2i)?

Back

To add complex numbers, combine the real parts and the imaginary parts: (3 + 5) + (4i + 2i) = 8 + 6i.

Tags

CCSS.HSN.CN.A.2

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